Preference-based Semantics for Nonmonotonic Logics

A variant is proposed of the preference-based semantics for nonmonotonic logics that was originally considered by Shoham (1987,1988). In this variant it is not assumed that preferences between standard models are aggregated into one preference order. This allows the capturing of all main nonmonotonic formalisms, including Default Logic of Reiter (1980). The preferential models introduced in this paper are motivated from an epistemic point of view, and are therefore called epistemic preference models. The consequence operations induced by epistemic preference models are characterized. Further, the view is defended that the rationality of cumulative monotonicity does not imply that nonmonotonic logics have to be cumulative, but only that a rational agent should not believe a set of default rules that induces a noncumulative consequence operation